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<div class="subTitle">org.apache.commons.math3.linear</div>
<h2 title="Class ConjugateGradient" class="title">Class ConjugateGradient</h2>
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<li><a href="../../../../../org/apache/commons/math3/linear/IterativeLinearSolver.html" title="class in org.apache.commons.math3.linear">org.apache.commons.math3.linear.IterativeLinearSolver</a></li>
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<li><a href="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html" title="class in org.apache.commons.math3.linear">org.apache.commons.math3.linear.PreconditionedIterativeLinearSolver</a></li>
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<pre>public class <span class="strong">ConjugateGradient</span>
extends <a href="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html" title="class in org.apache.commons.math3.linear">PreconditionedIterativeLinearSolver</a></pre>
<div class="block"><p>
 This is an implementation of the conjugate gradient method for
 <a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear"><code>RealLinearOperator</code></a>. It follows closely the template by <a
 href="#BARR1994">Barrett et al. (1994)</a> (figure 2.5). The linear system at
 hand is A &middot; x = b, and the residual is r = b - A &middot; x.
 </p>
 <h3><a id="stopcrit">Default stopping criterion</a></h3>
 <p>
 A default stopping criterion is implemented. The iterations stop when || r ||
 &le; &delta; || b ||, where b is the right-hand side vector, r the current
 estimate of the residual, and &delta; a user-specified tolerance. It should
 be noted that r is the so-called <em>updated</em> residual, which might
 differ from the true residual due to rounding-off errors (see e.g. <a
 href="#STRA2002">Strakos and Tichy, 2002</a>).
 </p>
 <h3>Iteration count</h3>
 <p>
 In the present context, an iteration should be understood as one evaluation
 of the matrix-vector product A &middot; x. The initialization phase therefore
 counts as one iteration.
 </p>
 <h3><a id="context">Exception context</a></h3>
 <p>
 Besides standard <a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception"><code>DimensionMismatchException</code></a>, this class might throw
 <a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteOperatorException.html" title="class in org.apache.commons.math3.linear"><code>NonPositiveDefiniteOperatorException</code></a> if the linear operator or
 the preconditioner are not positive definite. In this case, the
 <a href="../../../../../org/apache/commons/math3/exception/util/ExceptionContext.html" title="class in org.apache.commons.math3.exception.util"><code>ExceptionContext</code></a> provides some more information
 <ul>
 <li>key <code>"operator"</code> points to the offending linear operator, say L,</li>
 <li>key <code>"vector"</code> points to the offending vector, say x, such that
 x<sup>T</sup> &middot; L &middot; x < 0.</li>
 </ul>
 </p>
 <h3>References</h3>
 <dl>
 <dt><a id="BARR1994">Barret et al. (1994)</a></dt>
 <dd>R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. M. Donato, J. Dongarra,
 V. Eijkhout, R. Pozo, C. Romine and H. Van der Vorst,
 <a href="http://www.netlib.org/linalg/html_templates/Templates.html"><em>
 Templates for the Solution of Linear Systems: Building Blocks for Iterative
 Methods</em></a>, SIAM</dd>
 <dt><a id="STRA2002">Strakos and Tichy (2002)
 <dt>
 <dd>Z. Strakos and P. Tichy, <a
 href="http://etna.mcs.kent.edu/vol.13.2002/pp56-80.dir/pp56-80.pdf">
 <em>On error estimation in the conjugate gradient method and why it works
 in finite precision computations</em></a>, Electronic Transactions on
 Numerical Analysis 13: 56-80, 2002</dd>
 </dl></div>
<dl><dt><span class="strong">Since:</span></dt>
  <dd>3.0</dd></dl>
</li>
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<tr>
<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Field and Description</th>
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<tr class="altColor">
<td class="colFirst"><code>static <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/ConjugateGradient.html#OPERATOR">OPERATOR</a></strong></code>
<div class="block">Key for the <a href="#context">exception context</a>.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/ConjugateGradient.html#VECTOR">VECTOR</a></strong></code>
<div class="block">Key for the <a href="#context">exception context</a>.</div>
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<th class="colOne" scope="col">Constructor and Description</th>
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<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/linear/ConjugateGradient.html#ConjugateGradient(int,%20double,%20boolean)">ConjugateGradient</a></strong>(int&nbsp;maxIterations,
                 double&nbsp;delta,
                 boolean&nbsp;check)</code>
<div class="block">Creates a new instance of this class, with <a href="#stopcrit">default
 stopping criterion</a>.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/linear/ConjugateGradient.html#ConjugateGradient(org.apache.commons.math3.util.IterationManager,%20double,%20boolean)">ConjugateGradient</a></strong>(<a href="../../../../../org/apache/commons/math3/util/IterationManager.html" title="class in org.apache.commons.math3.util">IterationManager</a>&nbsp;manager,
                 double&nbsp;delta,
                 boolean&nbsp;check)</code>
<div class="block">Creates a new instance of this class, with <a href="#stopcrit">default
 stopping criterion</a> and custom iteration manager.</div>
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<th class="colFirst" scope="col">Modifier and Type</th>
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<td class="colFirst"><code>boolean</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/ConjugateGradient.html#getCheck()">getCheck</a></strong>()</code>
<div class="block">Returns <code>true</code> if positive-definiteness should be checked for both
 matrix and preconditioner.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/ConjugateGradient.html#solveInPlace(org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealVector,%20org.apache.commons.math3.linear.RealVector)">solveInPlace</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</a>&nbsp;a,
            <a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</a>&nbsp;m,
            <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a>&nbsp;b,
            <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a>&nbsp;x0)</code>
<div class="block">Returns an estimate of the solution to the linear system A &middot; x =
 b.</div>
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<code><a href="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html#checkParameters(org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealVector,%20org.apache.commons.math3.linear.RealVector)">checkParameters</a>, <a href="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html#solve(org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealVector)">solve</a>, <a href="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html#solve(org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealVector,%20org.apache.commons.math3.linear.RealVector)">solve</a>, <a href="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html#solve(org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealVector)">solve</a>, <a href="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html#solve(org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealVector,%20org.apache.commons.math3.linear.RealVector)">solve</a>, <a href="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html#solveInPlace(org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealVector,%20org.apache.commons.math3.linear.RealVector)">solveInPlace</a></code></li>
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<code><a href="../../../../../org/apache/commons/math3/linear/IterativeLinearSolver.html#checkParameters(org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealVector,%20org.apache.commons.math3.linear.RealVector)">checkParameters</a>, <a href="../../../../../org/apache/commons/math3/linear/IterativeLinearSolver.html#getIterationManager()">getIterationManager</a></code></li>
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<h3>Methods inherited from class&nbsp;java.lang.<a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></h3>
<code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait(long,%20int)" title="class or interface in java.lang">wait</a></code></li>
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<h4>OPERATOR</h4>
<pre>public static final&nbsp;<a href="http://docs.oracle.com/javase/7/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</a> OPERATOR</pre>
<div class="block">Key for the <a href="#context">exception context</a>.</div>
<dl><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../constant-values.html#org.apache.commons.math3.linear.ConjugateGradient.OPERATOR">Constant Field Values</a></dd></dl>
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<pre>public static final&nbsp;<a href="http://docs.oracle.com/javase/7/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</a> VECTOR</pre>
<div class="block">Key for the <a href="#context">exception context</a>.</div>
<dl><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../constant-values.html#org.apache.commons.math3.linear.ConjugateGradient.VECTOR">Constant Field Values</a></dd></dl>
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<h4>ConjugateGradient</h4>
<pre>public&nbsp;ConjugateGradient(int&nbsp;maxIterations,
                 double&nbsp;delta,
                 boolean&nbsp;check)</pre>
<div class="block">Creates a new instance of this class, with <a href="#stopcrit">default
 stopping criterion</a>.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>maxIterations</code> - the maximum number of iterations</dd><dd><code>delta</code> - the &delta; parameter for the default stopping criterion</dd><dd><code>check</code> - <code>true</code> if positive definiteness of both matrix and
 preconditioner should be checked</dd></dl>
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<pre>public&nbsp;ConjugateGradient(<a href="../../../../../org/apache/commons/math3/util/IterationManager.html" title="class in org.apache.commons.math3.util">IterationManager</a>&nbsp;manager,
                 double&nbsp;delta,
                 boolean&nbsp;check)
                  throws <a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></pre>
<div class="block">Creates a new instance of this class, with <a href="#stopcrit">default
 stopping criterion</a> and custom iteration manager.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>manager</code> - the custom iteration manager</dd><dd><code>delta</code> - the &delta; parameter for the default stopping criterion</dd><dd><code>check</code> - <code>true</code> if positive definiteness of both matrix and
 preconditioner should be checked</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if <code>manager</code> is <code>null</code></dd></dl>
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<pre>public final&nbsp;boolean&nbsp;getCheck()</pre>
<div class="block">Returns <code>true</code> if positive-definiteness should be checked for both
 matrix and preconditioner.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd><code>true</code> if the tests are to be performed</dd></dl>
</li>
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<a name="solveInPlace(org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealLinearOperator, org.apache.commons.math3.linear.RealVector, org.apache.commons.math3.linear.RealVector)">
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<pre>public&nbsp;<a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a>&nbsp;solveInPlace(<a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</a>&nbsp;a,
                      <a href="../../../../../org/apache/commons/math3/linear/RealLinearOperator.html" title="class in org.apache.commons.math3.linear">RealLinearOperator</a>&nbsp;m,
                      <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a>&nbsp;b,
                      <a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a>&nbsp;x0)
                        throws <a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>,
                               <a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteOperatorException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteOperatorException</a>,
                               <a href="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</a>,
                               <a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>,
                               <a href="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></pre>
<div class="block">Returns an estimate of the solution to the linear system A &middot; x =
 b. The solution is computed in-place (initial guess is modified).</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html#solveInPlace(org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealLinearOperator,%20org.apache.commons.math3.linear.RealVector,%20org.apache.commons.math3.linear.RealVector)">solveInPlace</a></code>&nbsp;in class&nbsp;<code><a href="../../../../../org/apache/commons/math3/linear/PreconditionedIterativeLinearSolver.html" title="class in org.apache.commons.math3.linear">PreconditionedIterativeLinearSolver</a></code></dd>
<dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - the linear operator A of the system</dd><dd><code>m</code> - the preconditioner, M (can be <code>null</code>)</dd><dd><code>b</code> - the right-hand side vector</dd><dd><code>x0</code> - the initial guess of the solution</dd>
<dt><span class="strong">Returns:</span></dt><dd>a reference to <code>x0</code> (shallow copy) updated with the
 solution</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteOperatorException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteOperatorException</a></code> - if <code>a</code> or <code>m</code> is
 not positive definite</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if one of the parameters is <code>null</code></dd>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSquareOperatorException.html" title="class in org.apache.commons.math3.linear">NonSquareOperatorException</a></code> - if <code>a</code> or <code>m</code> is not
 square</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if <code>m</code>, <code>b</code> or
 <code>x0</code> have dimensions inconsistent with <code>a</code></dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</a></code> - at exhaustion of the iteration count,
 unless a custom
 <a href="../../../../../org/apache/commons/math3/util/Incrementor.MaxCountExceededCallback.html" title="interface in org.apache.commons.math3.util"><code>callback</code></a>
 has been set at construction of the <a href="../../../../../org/apache/commons/math3/util/IterationManager.html" title="class in org.apache.commons.math3.util"><code>IterationManager</code></a></dd></dl>
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